Sentence examples for be defined below from inspiring English sources

For illustration, the map of our preferred u s (in a sense to be defined below) is shown in Fig. 3a.

The following results show that the two models can be distinguished for parameter values such that the two models are sufficiently different, which will be defined below in Sect.

Our aim in this work is to prove the cross-ratio inequality for a new class of circle homeomorphisms, which will be defined below with the aid of the above two classes and to show the existence of a conjugating map for this new class.

First, for a given width of the temporal window over which the model is meant to be computed (that will be defined below), we iteratively adjusted the bounding epochs in order to have an arithmetic mean epoch equal to 2005.0, within an arbitrary tolerance of ±0.042 yr (±15 days), and an equal amount of data before and after 2005.0.

We introduce the following iteration scheme: and the convergence of the sequence { ( u n, v n ) } follows by showing that { Φ 1 ( v ) = ∫ 0 t ∫ Ω g ( x, y, t − s ) a 1 ( y ) v n p 1 ( y ) d y d s, Φ 2 ( u ) = ∫ 0 t ∫ Ω g ( x, y, t − s ) a 2 ( y ) u n p 2 ( y ) d y d s. is a contraction in the set E T to be defined below.

Furthermore, if an optimal data set (to be defined below) is used, some high degree monomials will never be among the candidates.

These assumptions guarantee the Markov chain that is defined below is irreducible and a periodic.

Satisfactory progress is defined below.

This development led to mean solar time as the norm; it is defined below.

In the following report, the causal analysis methodology is defined below, and one case study is presented.

Based on these arguments, a critical Karlovitz number is defined, below which dilatation effects are expected to become significant.